Apply Other Angle Relationships in Circles Lesson 10-5 Apply Other Angle Relationships in Circles

Angles Inside the Circle Theorem (Interior Angle Theorem) Definition: Angles that are formed by two intersecting chords. 1 A B C D 2 E Interior Angle Theorem: The measure of the angle formed by the two intersecting chords is equal to ½ the sum of the measures of the intercepted arcs.

Example: Interior Angle Theorem 91 A C x° y° B D 85

Practice: 1) 2)

Exterior Angles An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. 3 y ° x 2 1 Two secants 2 tangents A secant and a tangent

Angles Outside the Circle Theorem (Exterior Angle Theorem) The measure of the angle formed is equal to ½ the difference of the intercepted arcs.

Example: Exterior Angle Theorem

Q G F D E C 1 2 3 4 5 6 A 30° 25° 100°

Practice: 1) 2)

An Angle Formed by a Chord and a Tangent If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

Practice: 1) 2)